Mathematics

In the diagram given below $$\angle EDC$$. The tangent drawn to the circle at $$C$$ makes and angle of $${50}^{o}$$ with $$AB$$ produced. Find the measure of $$\angle ACB$$.


SOLUTION
$$\angle{AGE}={50}^{\circ}$$
Consider $$AC$$ diameter
In $$\triangle{ACG},\angle{ACG}={90}^{\circ}$$
$$\Rightarrow \angle{CAG}={40}^{\circ}$$
In $$\triangle{ACB},\angle{CAB}={40}^{\circ}$$
$$\Rightarrow \angle{ACB}={50}^{\circ}$$
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